state of the economy	probability of occurrence	expected return on stock A	expected return on stock B
High growth	0.1	60%	5%
Moderate growth	0.2	20%	20%
No growth	0.5	10%	5%
Recession	0.2	-25%	0%

1)Calculate the weighted average of the standard deviation of individual stocks A and B ; and show that each portfolio standard deviation is less than this weighted average except the portfolio standard deviation with correlation of 1.

2) Given correlation of -1, what portfolio weights will reduce the portfolio standard deviation to zero? Show calculations to support your answer.